There are four married couples and eight seats. When they sit, what is the probability that husband sits adjacent to his wife?
The answer to this problem is 12/35
I can arrive at this answer when I ...

I believe the most restrictive assumption we can place on a series of observations is that they are iid.
It is possible to relax these assumptions. For example relaxing the independent distribution ...

Suppose that the time students wait for a bus can be described by a uniform random variable X, where X is between 0 minutes and 60 minutes.
a) sketch the density function
b) what is the probability ...

I am wondering how to define a scalar generalization of variance for multi-dimensionnal random variables. In the case of simple multi-dimensionnal spaces where all dimensions have a similar behaviour, ...

Consider that $P$ is the water pressure coming out from a valve A, therefore, the population is all the valve A pressure values. Let $P_{dif}$ be defined as the difference between the maximum and the ...

When given a mean and variance of a sample, without knowing the observations, how would you then find the new mean and variance given more observations?
Any help with this would be much appreciated.
...

For a trip to be successfully launched, 100 different parts on the ship must all be functioning properly. The probability for each parts failing, $p$, is $0.0001$.
i. What is the probability that the ...

who can help me to resolution of this statistic exercise?
below the track:
Caio go in a bank,the number of customers ahead him are described by a Poisson random variable of parameter a>0.
Calculate ...

Let's say, I have an autocorrelation function:
$$C(\text{lag}) = \text{lag}^{-\gamma}$$
How can I generate a sample of a time series of, say, $0$'s and $1$'s, such that their sample autocorrelation ...

The scores of a final exam have a Normal Distribution with mean $75$ and standard deviation 6. An independent sample size of $9$ is drawn from this distribution. The corresponding random variables are ...

Based on a random sample of 20 values from a normal distribution with mean $\mu$ and variance $\sigma^{2}$, it was calculated that $\bar{X}=8$ and $s=4$. Provide a $95\%$ confidence interval for the ...

"A soldier can hide in one of five foxholes, and a gunner can hide in four spots: A, B C, and D. The configuration looks like this: 1 (A) 2 (B) 3 (C) 4 (D) 5. If a shot is fired at a location and the ...

A gambler tosses a coin repeatedly until it comes up tails. He gets £1 for each head that comes up before that happens, and pays back £1 for the tail. Find the probability generating function for his ...

I was wondering if any one of you had any intuitive insight regarding the conditional probability equation, $P(A\mid B) = \large \frac{P(A \cap B)}{P(B)}$. In my textbook, they give a mere definition, ...

The problem I am currently working on is:
In five-card poker, a straight consists of five cards with adja-cent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king ...

So I'm working on a question that wants me to consider the sample mean $\mu_1$ (estimator of $\mu$) when $n=3$ to be $μ_1=X_1+X_2+X_3$. Now first I assume that they are independently and identically ...